Find the values of a and b for the function y = 2x3 + ax2 + bx given critical points at x=2 and x=1.

Step 1: Answer Question 1.a.

• What do you mean by the minimum point of a function? A minimum point of a function is a point on its graph where the function's value is less than or equal to the values at all nearby points (local minimum) or all points in its domain (global minimum). At a local minimum, the first derivative of the function is zero, and the second derivative is positive.

• The function $y = 2x^3 + ax^2 + bx$ where $a$ and $b$ are constants, has critical points at $x=2$ and $x=1$.

  • **(i) Find the values of $a$ and $b